# Import required libraries
import pandas as pd
import numpy as np
from google.colab import files
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller, kpss
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.vector_ar.vecm import coint_johansen
import matplotlib.pyplot as plt

# Upload Excel files
print("Please upload MS Excel file")
MS_upload = files.upload()
MS_filename = list(MS_upload.keys())[0]
MS_df = pd.read_excel(MS_filename)

print("Please upload JPM Excel file")
JPM_upload = files.upload()
JPM_filename = list(JPM_upload.keys())[0]
JPM_df = pd.read_excel(JPM_filename)

print("Please upload LMT Excel file")
LMT_upload = files.upload()
LMT_filename = list(LMT_upload.keys())[0]
LMT_df = pd.read_excel(LMT_filename)

# Print available columns
print("\nMS DataFrame columns:", list(MS_df.columns))
print("JPM DataFrame columns:", list(JPM_df.columns))
print("LMT DataFrame columns:", list(LMT_df.columns))

# Ask user for the correct column name
close_column = input("Please enter the column name containing closing prices: ")

# Extract closing prices using user-specified column name
try:
    MS_close = MS_df[close_column]
    JPM_close = JPM_df[close_column]
    LMT_close = LMT_df[close_column]
except KeyError:
    print(f"Error: Column '{close_column}' not found in one or more DataFrames")
    print("Please check the column names and try again")
    raise

# Ensure all series have the same length
min_length = min(len(MS_close), len(JPM_close), len(LMT_close))
MS_close = MS_close[:min_length]
JPM_close = JPM_close[:min_length]
LMT_close = LMT_close[:min_length]

# Function for unit root tests
def unit_root_tests(series, name):
    print(f"\nUnit Root Tests for {name}:")

    # ADF Test
    adf_result = adfuller(series)
    print("ADF Test:")
    print(f'ADF Statistic: {adf_result[0]:.4f}')
    print(f'p-value: {adf_result[1]:.4f}')
    print(f'Critical Values: {adf_result[4]}')

    # KPSS Test
    kpss_result = kpss(series)
    print("\nKPSS Test:")
    print(f'KPSS Statistic: {kpss_result[0]:.4f}')
    print(f'p-value: {kpss_result[1]:.4f}')
    print(f'Critical Values: {kpss_result[3]}')

# Perform unit root tests
unit_root_tests(MS_close, "MS")
unit_root_tests(JPM_close, "JPM")
unit_root_tests(LMT_close, "LMT")

# Difference the series if non-stationary
MS_diff = MS_close.diff().dropna()
JPM_diff = JPM_close.diff().dropna()
LMT_diff = LMT_close.diff().dropna()

# Function to find best ARMA model (using ARIMA with d=0)
def find_best_arma(series, name, max_p=3, max_q=3):
    best_aic = float('inf')
    best_order = None

    for p in range(max_p + 1):
        for q in range(max_q + 1):
            try:
                model = ARIMA(series, order=(p, 0, q))
                results = model.fit()
                if results.aic < best_aic:
                    best_aic = results.aic
                    best_order = (p, 0, q)
            except:
                continue

    print(f"\nBest ARMA model for {name}:")
    print(f"Order: {best_order}")
    print(f"AIC: {best_aic:.2f}")

    best_model = ARIMA(series, order=best_order).fit()
    return best_model

# Fit ARMA models
MS_arma = find_best_arma(MS_diff, "MS")
JPM_arma = find_best_arma(JPM_diff, "JPM")
LMT_arma = find_best_arma(LMT_diff, "LMT")

# Cointegration test
def cointegration_test(df):
    result = coint_johansen(df, det_order=0, k_ar_diff=1)
    print("\nJohansen Cointegration Test:")
    print(f"Trace statistic: {result.lr1}")
    print(f"Critical values (90%, 95%, 99%): {result.cvt}")

    for i in range(len(result.lr1)):
        if result.lr1[i] > result.cvt[i, 1]:  # 95% critical value
            print(f"r = {i}: Cointegration exists at 95% confidence level")
        else:
            print(f"r = {i}: No cointegration at 95% confidence level")

# Prepare data for cointegration
coint_df = pd.DataFrame({
    'MS': MS_close,
    'JPM': JPM_close,
    'LMT': LMT_close
}).dropna()

# Run cointegration test
cointegration_test(coint_df)

# Plot the series
plt.figure(figsize=(12,6))
plt.plot(MS_close, label='MS')
plt.plot(JPM_close, label='JPM')
plt.plot(LMT_close, label='LMT')
plt.title('MS vs JPM vs LMT Closing Prices')
plt.legend()
plt.show()

# Plot the differenced series
plt.figure(figsize=(12,6))
plt.plot(MS_diff, label='MS Diff')
plt.plot(JPM_diff, label='JPM Diff')
plt.plot(LMT_diff, label='LMT Diff')
plt.title('Differenced Series')
plt.legend()
plt.show()

Please upload MS Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving MS 3D 3M.xlsx to MS 3D 3M.xlsx
Please upload JPM Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving JPM 3D 3M.xlsx to JPM 3D 3M.xlsx
Please upload LMT Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving LMT 3D 3M.xlsx to LMT 3D 3M.xlsx

MS DataFrame columns: ['FECHA', 'PRECIO']
JPM DataFrame columns: ['FECHA', 'PRECIO']
LMT DataFrame columns: ['FECHA', 'PRECIO']
Please enter the column name containing closing prices: PRECIO

Unit Root Tests for MS:
ADF Test:
ADF Statistic: -1.7909
p-value: 0.3850
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 1.9167
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for JPM:
ADF Test:
ADF Statistic: -1.6691
p-value: 0.4471
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 2.3696
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for LMT:
ADF Test:
ADF Statistic: -3.1254
p-value: 0.0247
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 1.5833
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

<ipython-input-15-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-15-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-15-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for MS:
Order: (1, 0, 2)
AIC: 148.83

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'

Best ARMA model for JPM:
Order: (3, 0, 2)
AIC: 619.17

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for LMT:
Order: (0, 0, 0)
AIC: 880.11

Johansen Cointegration Test:
Trace statistic: [58.57171949 15.88982446  4.8846984 ]
Critical values (90%, 95%, 99%): [[27.0669 29.7961 35.4628]
 [13.4294 15.4943 19.9349]
 [ 2.7055  3.8415  6.6349]]
r = 0: Cointegration exists at 95% confidence level
r = 1: Cointegration exists at 95% confidence level
r = 2: Cointegration exists at 95% confidence level

# Import required libraries
import pandas as pd
import numpy as np
from google.colab import files
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller, kpss
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.vector_ar.vecm import coint_johansen
import matplotlib.pyplot as plt

# Upload Excel files
print("Please upload MS Excel file")
MS_upload = files.upload()
MS_filename = list(MS_upload.keys())[0]
MS_df = pd.read_excel(MS_filename)

print("Please upload JPM Excel file")
JPM_upload = files.upload()
JPM_filename = list(JPM_upload.keys())[0]
JPM_df = pd.read_excel(JPM_filename)

print("Please upload LMT Excel file")
LMT_upload = files.upload()
LMT_filename = list(LMT_upload.keys())[0]
LMT_df = pd.read_excel(LMT_filename)

# Print available columns
print("\nMS DataFrame columns:", list(MS_df.columns))
print("JPM DataFrame columns:", list(JPM_df.columns))
print("LMT DataFrame columns:", list(LMT_df.columns))

# Ask user for the correct column name
close_column = input("Please enter the column name containing closing prices: ")

# Extract closing prices using user-specified column name
try:
    MS_close = MS_df[close_column]
    JPM_close = JPM_df[close_column]
    LMT_close = LMT_df[close_column]
except KeyError:
    print(f"Error: Column '{close_column}' not found in one or more DataFrames")
    print("Please check the column names and try again")
    raise

# Ensure all series have the same length
min_length = min(len(MS_close), len(JPM_close), len(LMT_close))
MS_close = MS_close[:min_length]
JPM_close = JPM_close[:min_length]
LMT_close = LMT_close[:min_length]

# Function for unit root tests
def unit_root_tests(series, name):
    print(f"\nUnit Root Tests for {name}:")

    # ADF Test
    adf_result = adfuller(series)
    print("ADF Test:")
    print(f'ADF Statistic: {adf_result[0]:.4f}')
    print(f'p-value: {adf_result[1]:.4f}')
    print(f'Critical Values: {adf_result[4]}')

    # KPSS Test
    kpss_result = kpss(series)
    print("\nKPSS Test:")
    print(f'KPSS Statistic: {kpss_result[0]:.4f}')
    print(f'p-value: {kpss_result[1]:.4f}')
    print(f'Critical Values: {kpss_result[3]}')

# Perform unit root tests
unit_root_tests(MS_close, "MS")
unit_root_tests(JPM_close, "JPM")
unit_root_tests(LMT_close, "LMT")

# Difference the series if non-stationary
MS_diff = MS_close.diff().dropna()
JPM_diff = JPM_close.diff().dropna()
LMT_diff = LMT_close.diff().dropna()

# Function to find best ARMA model (using ARIMA with d=0)
def find_best_arma(series, name, max_p=3, max_q=3):
    best_aic = float('inf')
    best_order = None

    for p in range(max_p + 1):
        for q in range(max_q + 1):
            try:
                model = ARIMA(series, order=(p, 0, q))
                results = model.fit()
                if results.aic < best_aic:
                    best_aic = results.aic
                    best_order = (p, 0, q)
            except:
                continue

    print(f"\nBest ARMA model for {name}:")
    print(f"Order: {best_order}")
    print(f"AIC: {best_aic:.2f}")

    best_model = ARIMA(series, order=best_order).fit()
    return best_model

# Fit ARMA models
MS_arma = find_best_arma(MS_diff, "MS")
JPM_arma = find_best_arma(JPM_diff, "JPM")
LMT_arma = find_best_arma(LMT_diff, "LMT")

# Cointegration test
def cointegration_test(df):
    result = coint_johansen(df, det_order=0, k_ar_diff=1)
    print("\nJohansen Cointegration Test:")
    print(f"Trace statistic: {result.lr1}")
    print(f"Critical values (90%, 95%, 99%): {result.cvt}")

    for i in range(len(result.lr1)):
        if result.lr1[i] > result.cvt[i, 1]:  # 95% critical value
            print(f"r = {i}: Cointegration exists at 95% confidence level")
        else:
            print(f"r = {i}: No cointegration at 95% confidence level")

# Prepare data for cointegration
coint_df = pd.DataFrame({
    'MS': MS_close,
    'JPM': JPM_close,
    'LMT': LMT_close
}).dropna()

# Run cointegration test
cointegration_test(coint_df)

# Plot the series
plt.figure(figsize=(12,6))
plt.plot(MS_close, label='MS')
plt.plot(JPM_close, label='JPM')
plt.plot(LMT_close, label='LMT')
plt.title('MS vs JPM vs LMT Closing Prices')
plt.legend()
plt.show()

# Plot the differenced series
plt.figure(figsize=(12,6))
plt.plot(MS_diff, label='MS Diff')
plt.plot(JPM_diff, label='JPM Diff')
plt.plot(LMT_diff, label='LMT Diff')
plt.title('Differenced Series')
plt.legend()
plt.show()

Please upload MS Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving MS 3D 3M.xlsx to MS 3D 3M (1).xlsx
Please upload JPM Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving JPM 3D 3M.xlsx to JPM 3D 3M (1).xlsx
Please upload LMT Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving LMT 3D 3M.xlsx to LMT 3D 3M (1).xlsx

MS DataFrame columns: ['FECHA', 'PRECIO']
JPM DataFrame columns: ['FECHA', 'PRECIO']
LMT DataFrame columns: ['FECHA', 'PRECIO']
Please enter the column name containing closing prices: PRECIO

Unit Root Tests for MS:
ADF Test:
ADF Statistic: -1.7909
p-value: 0.3850
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 1.9167
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for JPM:
ADF Test:
ADF Statistic: -1.6691
p-value: 0.4471
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 2.3696
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for LMT:
ADF Test:
ADF Statistic: -3.1254
p-value: 0.0247
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 1.5833
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

<ipython-input-16-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-16-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-16-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for MS:
Order: (1, 0, 2)
AIC: 148.83

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'

Best ARMA model for JPM:
Order: (3, 0, 2)
AIC: 619.17

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for LMT:
Order: (0, 0, 0)
AIC: 880.11

Johansen Cointegration Test:
Trace statistic: [58.57171949 15.88982446  4.8846984 ]
Critical values (90%, 95%, 99%): [[27.0669 29.7961 35.4628]
 [13.4294 15.4943 19.9349]
 [ 2.7055  3.8415  6.6349]]
r = 0: Cointegration exists at 95% confidence level
r = 1: Cointegration exists at 95% confidence level
r = 2: Cointegration exists at 95% confidence level

# Import required libraries
import pandas as pd
import numpy as np
from google.colab import files
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller, kpss
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.vector_ar.vecm import coint_johansen
import matplotlib.pyplot as plt

# Upload Excel files
print("Please upload MS Excel file")
MS_upload = files.upload()
MS_filename = list(MS_upload.keys())[0]
MS_df = pd.read_excel(MS_filename)

print("Please upload JPM Excel file")
JPM_upload = files.upload()
JPM_filename = list(JPM_upload.keys())[0]
JPM_df = pd.read_excel(JPM_filename)

print("Please upload LMT Excel file")
LMT_upload = files.upload()
LMT_filename = list(LMT_upload.keys())[0]
LMT_df = pd.read_excel(LMT_filename)

# Print available columns
print("\nMS DataFrame columns:", list(MS_df.columns))
print("JPM DataFrame columns:", list(JPM_df.columns))
print("LMT DataFrame columns:", list(LMT_df.columns))

# Ask user for the correct column name
close_column = input("Please enter the column name containing closing prices: ")

# Extract closing prices using user-specified column name
try:
    MS_close = MS_df[close_column]
    JPM_close = JPM_df[close_column]
    LMT_close = LMT_df[close_column]
except KeyError:
    print(f"Error: Column '{close_column}' not found in one or more DataFrames")
    print("Please check the column names and try again")
    raise

# Ensure all series have the same length
min_length = min(len(MS_close), len(JPM_close), len(LMT_close))
MS_close = MS_close[:min_length]
JPM_close = JPM_close[:min_length]
LMT_close = LMT_close[:min_length]

# Function for unit root tests
def unit_root_tests(series, name):
    print(f"\nUnit Root Tests for {name}:")

    # ADF Test
    adf_result = adfuller(series)
    print("ADF Test:")
    print(f'ADF Statistic: {adf_result[0]:.4f}')
    print(f'p-value: {adf_result[1]:.4f}')
    print(f'Critical Values: {adf_result[4]}')

    # KPSS Test
    kpss_result = kpss(series)
    print("\nKPSS Test:")
    print(f'KPSS Statistic: {kpss_result[0]:.4f}')
    print(f'p-value: {kpss_result[1]:.4f}')
    print(f'Critical Values: {kpss_result[3]}')

# Perform unit root tests
unit_root_tests(MS_close, "MS")
unit_root_tests(JPM_close, "JPM")
unit_root_tests(LMT_close, "LMT")

# Difference the series if non-stationary
MS_diff = MS_close.diff().dropna()
JPM_diff = JPM_close.diff().dropna()
LMT_diff = LMT_close.diff().dropna()

# Function to find best ARMA model (using ARIMA with d=0)
def find_best_arma(series, name, max_p=3, max_q=3):
    best_aic = float('inf')
    best_order = None

    for p in range(max_p + 1):
        for q in range(max_q + 1):
            try:
                model = ARIMA(series, order=(p, 0, q))
                results = model.fit()
                if results.aic < best_aic:
                    best_aic = results.aic
                    best_order = (p, 0, q)
            except:
                continue

    print(f"\nBest ARMA model for {name}:")
    print(f"Order: {best_order}")
    print(f"AIC: {best_aic:.2f}")

    best_model = ARIMA(series, order=best_order).fit()
    return best_model

# Fit ARMA models
MS_arma = find_best_arma(MS_diff, "MS")
JPM_arma = find_best_arma(JPM_diff, "JPM")
LMT_arma = find_best_arma(LMT_diff, "LMT")

# Cointegration test
def cointegration_test(df):
    result = coint_johansen(df, det_order=0, k_ar_diff=1)
    print("\nJohansen Cointegration Test:")
    print(f"Trace statistic: {result.lr1}")
    print(f"Critical values (90%, 95%, 99%): {result.cvt}")

    for i in range(len(result.lr1)):
        if result.lr1[i] > result.cvt[i, 1]:  # 95% critical value
            print(f"r = {i}: Cointegration exists at 95% confidence level")
        else:
            print(f"r = {i}: No cointegration at 95% confidence level")

# Prepare data for cointegration
coint_df = pd.DataFrame({
    'MS': MS_close,
    'JPM': JPM_close,
    'LMT': LMT_close
}).dropna()

# Run cointegration test
cointegration_test(coint_df)

# Plot the series
plt.figure(figsize=(12,6))
plt.plot(MS_close, label='MS')
plt.plot(JPM_close, label='JPM')
plt.plot(LMT_close, label='LMT')
plt.title('MS vs JPM vs LMT Closing Prices')
plt.legend()
plt.show()

# Plot the differenced series
plt.figure(figsize=(12,6))
plt.plot(MS_diff, label='MS Diff')
plt.plot(JPM_diff, label='JPM Diff')
plt.plot(LMT_diff, label='LMT Diff')
plt.title('Differenced Series')
plt.legend()
plt.show()

Please upload MS Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving MS 3D 3M.xlsx to MS 3D 3M (2).xlsx
Please upload JPM Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving JPM 3D 3M.xlsx to JPM 3D 3M (2).xlsx
Please upload LMT Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving LMT 3D 3M.xlsx to LMT 3D 3M (2).xlsx

MS DataFrame columns: ['FECHA', 'PRECIO']
JPM DataFrame columns: ['FECHA', 'PRECIO']
LMT DataFrame columns: ['FECHA', 'PRECIO']
Please enter the column name containing closing prices: PRECIO

Unit Root Tests for MS:
ADF Test:
ADF Statistic: -1.7909
p-value: 0.3850
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 1.9167
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for JPM:
ADF Test:
ADF Statistic: -1.6691
p-value: 0.4471
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 2.3696
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for LMT:
ADF Test:
ADF Statistic: -3.1254
p-value: 0.0247
Critical Values: {'1%': -3.444932949082776, '5%': -2.867969899953726, '10%': -2.57019489663276}

KPSS Test:
KPSS Statistic: 1.5833
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

<ipython-input-17-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-17-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-17-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for MS:
Order: (1, 0, 2)
AIC: 148.83

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'

Best ARMA model for JPM:
Order: (3, 0, 2)
AIC: 619.17

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for LMT:
Order: (0, 0, 0)
AIC: 880.11

Johansen Cointegration Test:
Trace statistic: [58.57171949 15.88982446  4.8846984 ]
Critical values (90%, 95%, 99%): [[27.0669 29.7961 35.4628]
 [13.4294 15.4943 19.9349]
 [ 2.7055  3.8415  6.6349]]
r = 0: Cointegration exists at 95% confidence level
r = 1: Cointegration exists at 95% confidence level
r = 2: Cointegration exists at 95% confidence level

# Import required libraries
import pandas as pd
import numpy as np
from google.colab import files
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller, kpss
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.vector_ar.vecm import coint_johansen
import matplotlib.pyplot as plt

# Upload Excel files
print("Please upload MS Excel file")
MS_upload = files.upload()
MS_filename = list(MS_upload.keys())[0]
MS_df = pd.read_excel(MS_filename)

print("Please upload JPM Excel file")
JPM_upload = files.upload()
JPM_filename = list(JPM_upload.keys())[0]
JPM_df = pd.read_excel(JPM_filename)

print("Please upload LMT Excel file")
LMT_upload = files.upload()
LMT_filename = list(LMT_upload.keys())[0]
LMT_df = pd.read_excel(LMT_filename)

# Print available columns
print("\nMS DataFrame columns:", list(MS_df.columns))
print("JPM DataFrame columns:", list(JPM_df.columns))
print("LMT DataFrame columns:", list(LMT_df.columns))

# Ask user for the correct column name
close_column = input("Please enter the column name containing closing prices: ")

# Extract closing prices using user-specified column name
try:
    MS_close = MS_df[close_column]
    JPM_close = JPM_df[close_column]
    LMT_close = LMT_df[close_column]
except KeyError:
    print(f"Error: Column '{close_column}' not found in one or more DataFrames")
    print("Please check the column names and try again")
    raise

# Ensure all series have the same length
min_length = min(len(MS_close), len(JPM_close), len(LMT_close))
MS_close = MS_close[:min_length]
JPM_close = JPM_close[:min_length]
LMT_close = LMT_close[:min_length]

# Function for unit root tests
def unit_root_tests(series, name):
    print(f"\nUnit Root Tests for {name}:")

    # ADF Test
    adf_result = adfuller(series)
    print("ADF Test:")
    print(f'ADF Statistic: {adf_result[0]:.4f}')
    print(f'p-value: {adf_result[1]:.4f}')
    print(f'Critical Values: {adf_result[4]}')

    # KPSS Test
    kpss_result = kpss(series)
    print("\nKPSS Test:")
    print(f'KPSS Statistic: {kpss_result[0]:.4f}')
    print(f'p-value: {kpss_result[1]:.4f}')
    print(f'Critical Values: {kpss_result[3]}')

# Perform unit root tests
unit_root_tests(MS_close, "MS")
unit_root_tests(JPM_close, "JPM")
unit_root_tests(LMT_close, "LMT")

# Difference the series if non-stationary
MS_diff = MS_close.diff().dropna()
JPM_diff = JPM_close.diff().dropna()
LMT_diff = LMT_close.diff().dropna()

# Function to find best ARMA model (using ARIMA with d=0)
def find_best_arma(series, name, max_p=3, max_q=3):
    best_aic = float('inf')
    best_order = None

    for p in range(max_p + 1):
        for q in range(max_q + 1):
            try:
                model = ARIMA(series, order=(p, 0, q))
                results = model.fit()
                if results.aic < best_aic:
                    best_aic = results.aic
                    best_order = (p, 0, q)
            except:
                continue

    print(f"\nBest ARMA model for {name}:")
    print(f"Order: {best_order}")
    print(f"AIC: {best_aic:.2f}")

    best_model = ARIMA(series, order=best_order).fit()
    return best_model

# Fit ARMA models
MS_arma = find_best_arma(MS_diff, "MS")
JPM_arma = find_best_arma(JPM_diff, "JPM")
LMT_arma = find_best_arma(LMT_diff, "LMT")

# Cointegration test
def cointegration_test(df):
    result = coint_johansen(df, det_order=0, k_ar_diff=1)
    print("\nJohansen Cointegration Test:")
    print(f"Trace statistic: {result.lr1}")
    print(f"Critical values (90%, 95%, 99%): {result.cvt}")

    for i in range(len(result.lr1)):
        if result.lr1[i] > result.cvt[i, 1]:  # 95% critical value
            print(f"r = {i}: Cointegration exists at 95% confidence level")
        else:
            print(f"r = {i}: No cointegration at 95% confidence level")

# Prepare data for cointegration
coint_df = pd.DataFrame({
    'MS': MS_close,
    'JPM': JPM_close,
    'LMT': LMT_close
}).dropna()

# Run cointegration test
cointegration_test(coint_df)

# Plot the series
plt.figure(figsize=(12,6))
plt.plot(MS_close, label='MS')
plt.plot(JPM_close, label='JPM')
plt.plot(LMT_close, label='LMT')
plt.title('MS vs JPM vs LMT Closing Prices')
plt.legend()
plt.show()

# Plot the differenced series
plt.figure(figsize=(12,6))
plt.plot(MS_diff, label='MS Diff')
plt.plot(JPM_diff, label='JPM Diff')
plt.plot(LMT_diff, label='LMT Diff')
plt.title('Differenced Series')
plt.legend()
plt.show()

Please upload MS Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving MS 10D 30M.xlsx to MS 10D 30M.xlsx
Please upload JPM Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving JPM 10D 30M.xlsx to JPM 10D 30M.xlsx
Please upload LMT Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving LMT 10D 30M.xlsx to LMT 10D 30M.xlsx

MS DataFrame columns: ['FECHA', 'PRECIO']
JPM DataFrame columns: ['FECHA', 'PRECIO']
LMT DataFrame columns: ['FECHA', 'PRECIO']
Please enter the column name containing closing prices: PRECIO

Unit Root Tests for MS:
ADF Test:
ADF Statistic: -1.2926
p-value: 0.6326
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.3195
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for JPM:
ADF Test:
ADF Statistic: -1.1067
p-value: 0.7124
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.3509
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for LMT:
ADF Test:
ADF Statistic: -2.6615
p-value: 0.0809
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.5835
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

<ipython-input-18-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-18-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-18-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'

Best ARMA model for MS:
Order: (0, 0, 0)
AIC: 405.74

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for JPM:
Order: (0, 0, 0)
AIC: 552.18

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for LMT:
Order: (0, 0, 0)
AIC: 605.67

Johansen Cointegration Test:
Trace statistic: [23.67197287  7.77838754  1.02627118]
Critical values (90%, 95%, 99%): [[27.0669 29.7961 35.4628]
 [13.4294 15.4943 19.9349]
 [ 2.7055  3.8415  6.6349]]
r = 0: No cointegration at 95% confidence level
r = 1: No cointegration at 95% confidence level
r = 2: No cointegration at 95% confidence level

# Import required libraries
import pandas as pd
import numpy as np
from google.colab import files
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller, kpss
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.vector_ar.vecm import coint_johansen
import matplotlib.pyplot as plt

# Upload Excel files
print("Please upload MS Excel file")
MS_upload = files.upload()
MS_filename = list(MS_upload.keys())[0]
MS_df = pd.read_excel(MS_filename)

print("Please upload JPM Excel file")
JPM_upload = files.upload()
JPM_filename = list(JPM_upload.keys())[0]
JPM_df = pd.read_excel(JPM_filename)

print("Please upload LMT Excel file")
LMT_upload = files.upload()
LMT_filename = list(LMT_upload.keys())[0]
LMT_df = pd.read_excel(LMT_filename)

# Print available columns
print("\nMS DataFrame columns:", list(MS_df.columns))
print("JPM DataFrame columns:", list(JPM_df.columns))
print("LMT DataFrame columns:", list(LMT_df.columns))

# Ask user for the correct column name
close_column = input("Please enter the column name containing closing prices: ")

# Extract closing prices using user-specified column name
try:
    MS_close = MS_df[close_column]
    JPM_close = JPM_df[close_column]
    LMT_close = LMT_df[close_column]
except KeyError:
    print(f"Error: Column '{close_column}' not found in one or more DataFrames")
    print("Please check the column names and try again")
    raise

# Ensure all series have the same length
min_length = min(len(MS_close), len(JPM_close), len(LMT_close))
MS_close = MS_close[:min_length]
JPM_close = JPM_close[:min_length]
LMT_close = LMT_close[:min_length]

# Function for unit root tests
def unit_root_tests(series, name):
    print(f"\nUnit Root Tests for {name}:")

    # ADF Test
    adf_result = adfuller(series)
    print("ADF Test:")
    print(f'ADF Statistic: {adf_result[0]:.4f}')
    print(f'p-value: {adf_result[1]:.4f}')
    print(f'Critical Values: {adf_result[4]}')

    # KPSS Test
    kpss_result = kpss(series)
    print("\nKPSS Test:")
    print(f'KPSS Statistic: {kpss_result[0]:.4f}')
    print(f'p-value: {kpss_result[1]:.4f}')
    print(f'Critical Values: {kpss_result[3]}')

# Perform unit root tests
unit_root_tests(MS_close, "MS")
unit_root_tests(JPM_close, "JPM")
unit_root_tests(LMT_close, "LMT")

# Difference the series if non-stationary
MS_diff = MS_close.diff().dropna()
JPM_diff = JPM_close.diff().dropna()
LMT_diff = LMT_close.diff().dropna()

# Function to find best ARMA model (using ARIMA with d=0)
def find_best_arma(series, name, max_p=3, max_q=3):
    best_aic = float('inf')
    best_order = None

    for p in range(max_p + 1):
        for q in range(max_q + 1):
            try:
                model = ARIMA(series, order=(p, 0, q))
                results = model.fit()
                if results.aic < best_aic:
                    best_aic = results.aic
                    best_order = (p, 0, q)
            except:
                continue

    print(f"\nBest ARMA model for {name}:")
    print(f"Order: {best_order}")
    print(f"AIC: {best_aic:.2f}")

    best_model = ARIMA(series, order=best_order).fit()
    return best_model

# Fit ARMA models
MS_arma = find_best_arma(MS_diff, "MS")
JPM_arma = find_best_arma(JPM_diff, "JPM")
LMT_arma = find_best_arma(LMT_diff, "LMT")

# Cointegration test
def cointegration_test(df):
    result = coint_johansen(df, det_order=0, k_ar_diff=1)
    print("\nJohansen Cointegration Test:")
    print(f"Trace statistic: {result.lr1}")
    print(f"Critical values (90%, 95%, 99%): {result.cvt}")

    for i in range(len(result.lr1)):
        if result.lr1[i] > result.cvt[i, 1]:  # 95% critical value
            print(f"r = {i}: Cointegration exists at 95% confidence level")
        else:
            print(f"r = {i}: No cointegration at 95% confidence level")

# Prepare data for cointegration
coint_df = pd.DataFrame({
    'MS': MS_close,
    'JPM': JPM_close,
    'LMT': LMT_close
}).dropna()

# Run cointegration test
cointegration_test(coint_df)

# Plot the series
plt.figure(figsize=(12,6))
plt.plot(MS_close, label='MS')
plt.plot(JPM_close, label='JPM')
plt.plot(LMT_close, label='LMT')
plt.title('MS vs JPM vs LMT Closing Prices')
plt.legend()
plt.show()

# Plot the differenced series
plt.figure(figsize=(12,6))
plt.plot(MS_diff, label='MS Diff')
plt.plot(JPM_diff, label='JPM Diff')
plt.plot(LMT_diff, label='LMT Diff')
plt.title('Differenced Series')
plt.legend()
plt.show()

Please upload MS Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving MS 10D 30M.xlsx to MS 10D 30M (1).xlsx
Please upload JPM Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving JPM 10D 30M.xlsx to JPM 10D 30M (1).xlsx
Please upload LMT Excel file

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving LMT 10D 30M.xlsx to LMT 10D 30M (1).xlsx

MS DataFrame columns: ['FECHA', 'PRECIO']
JPM DataFrame columns: ['FECHA', 'PRECIO']
LMT DataFrame columns: ['FECHA', 'PRECIO']
Please enter the column name containing closing prices: PRECIO

Unit Root Tests for MS:
ADF Test:
ADF Statistic: -1.2926
p-value: 0.6326
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.3195
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for JPM:
ADF Test:
ADF Statistic: -1.1067
p-value: 0.7124
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.3509
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for LMT:
ADF Test:
ADF Statistic: -2.6615
p-value: 0.0809
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.5835
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

<ipython-input-19-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-19-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-19-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'

Best ARMA model for MS:
Order: (0, 0, 0)
AIC: 405.74

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for JPM:
Order: (0, 0, 0)
AIC: 552.18

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for LMT:
Order: (0, 0, 0)
AIC: 605.67

Johansen Cointegration Test:
Trace statistic: [23.67197287  7.77838754  1.02627118]
Critical values (90%, 95%, 99%): [[27.0669 29.7961 35.4628]
 [13.4294 15.4943 19.9349]
 [ 2.7055  3.8415  6.6349]]
r = 0: No cointegration at 95% confidence level
r = 1: No cointegration at 95% confidence level
r = 2: No cointegration at 95% confidence level

# Import required libraries
import pandas as pd
import numpy as np
from google.colab import files
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller, kpss
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.vector_ar.vecm import coint_johansen
import matplotlib.pyplot as plt

# Upload Excel files
print("Please upload MS Excel file")
MS_upload = files.upload()
MS_filename = list(MS_upload.keys())[0]
MS_df = pd.read_excel(MS_filename)

print("Please upload JPM Excel file")
JPM_upload = files.upload()
JPM_filename = list(JPM_upload.keys())[0]
JPM_df = pd.read_excel(JPM_filename)

print("Please upload LMT Excel file")
LMT_upload = files.upload()
LMT_filename = list(LMT_upload.keys())[0]
LMT_df = pd.read_excel(LMT_filename)

# Print available columns
print("\nMS DataFrame columns:", list(MS_df.columns))
print("JPM DataFrame columns:", list(JPM_df.columns))
print("LMT DataFrame columns:", list(LMT_df.columns))

# Ask user for the correct column name
close_column = input("Please enter the column name containing closing prices: ")

# Extract closing prices using user-specified column name
try:
    MS_close = MS_df[close_column]
    JPM_close = JPM_df[close_column]
    LMT_close = LMT_df[close_column]
except KeyError:
    print(f"Error: Column '{close_column}' not found in one or more DataFrames")
    print("Please check the column names and try again")
    raise

# Ensure all series have the same length
min_length = min(len(MS_close), len(JPM_close), len(LMT_close))
MS_close = MS_close[:min_length]
JPM_close = JPM_close[:min_length]
LMT_close = LMT_close[:min_length]

# Function for unit root tests
def unit_root_tests(series, name):
    print(f"\nUnit Root Tests for {name}:")

    # ADF Test
    adf_result = adfuller(series)
    print("ADF Test:")
    print(f'ADF Statistic: {adf_result[0]:.4f}')
    print(f'p-value: {adf_result[1]:.4f}')
    print(f'Critical Values: {adf_result[4]}')

    # KPSS Test
    kpss_result = kpss(series)
    print("\nKPSS Test:")
    print(f'KPSS Statistic: {kpss_result[0]:.4f}')
    print(f'p-value: {kpss_result[1]:.4f}')
    print(f'Critical Values: {kpss_result[3]}')

# Perform unit root tests
unit_root_tests(MS_close, "MS")
unit_root_tests(JPM_close, "JPM")
unit_root_tests(LMT_close, "LMT")

# Difference the series if non-stationary
MS_diff = MS_close.diff().dropna()
JPM_diff = JPM_close.diff().dropna()
LMT_diff = LMT_close.diff().dropna()

# Function to find best ARMA model (using ARIMA with d=0)
def find_best_arma(series, name, max_p=3, max_q=3):
    best_aic = float('inf')
    best_order = None

    for p in range(max_p + 1):
        for q in range(max_q + 1):
            try:
                model = ARIMA(series, order=(p, 0, q))
                results = model.fit()
                if results.aic < best_aic:
                    best_aic = results.aic
                    best_order = (p, 0, q)
            except:
                continue

    print(f"\nBest ARMA model for {name}:")
    print(f"Order: {best_order}")
    print(f"AIC: {best_aic:.2f}")

    best_model = ARIMA(series, order=best_order).fit()
    return best_model

# Fit ARMA models
MS_arma = find_best_arma(MS_diff, "MS")
JPM_arma = find_best_arma(JPM_diff, "JPM")
LMT_arma = find_best_arma(LMT_diff, "LMT")

# Cointegration test
def cointegration_test(df):
    result = coint_johansen(df, det_order=0, k_ar_diff=1)
    print("\nJohansen Cointegration Test:")
    print(f"Trace statistic: {result.lr1}")
    print(f"Critical values (90%, 95%, 99%): {result.cvt}")

    for i in range(len(result.lr1)):
        if result.lr1[i] > result.cvt[i, 1]:  # 95% critical value
            print(f"r = {i}: Cointegration exists at 95% confidence level")
        else:
            print(f"r = {i}: No cointegration at 95% confidence level")

# Prepare data for cointegration
coint_df = pd.DataFrame({
    'MS': MS_close,
    'JPM': JPM_close,
    'LMT': LMT_close
}).dropna()

# Run cointegration test
cointegration_test(coint_df)

# Plot the series
plt.figure(figsize=(12,6))
plt.plot(MS_close, label='MS')
plt.plot(JPM_close, label='JPM')
plt.plot(LMT_close, label='LMT')
plt.title('MS vs JPM vs LMT Closing Prices')
plt.legend()
plt.show()

# Plot the differenced series
plt.figure(figsize=(12,6))
plt.plot(MS_diff, label='MS Diff')
plt.plot(JPM_diff, label='JPM Diff')
plt.plot(LMT_diff, label='LMT Diff')
plt.title('Differenced Series')
plt.legend()
plt.show()

Please upload MS Excel file

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Saving MS 10D 30M.xlsx to MS 10D 30M (2).xlsx
Please upload JPM Excel file

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Saving JPM 10D 30M.xlsx to JPM 10D 30M (2).xlsx
Please upload LMT Excel file

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Saving LMT 10D 30M.xlsx to LMT 10D 30M (2).xlsx

MS DataFrame columns: ['FECHA', 'PRECIO']
JPM DataFrame columns: ['FECHA', 'PRECIO']
LMT DataFrame columns: ['FECHA', 'PRECIO']
Please enter the column name containing closing prices: PRECIO

Unit Root Tests for MS:
ADF Test:
ADF Statistic: -1.2926
p-value: 0.6326
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.3195
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for JPM:
ADF Test:
ADF Statistic: -1.1067
p-value: 0.7124
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.3509
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

Unit Root Tests for LMT:
ADF Test:
ADF Statistic: -2.6615
p-value: 0.0809
Critical Values: {'1%': -3.4750180242954167, '5%': -2.8811408028842043, '10%': -2.577221358046935}

KPSS Test:
KPSS Statistic: 1.5835
p-value: 0.0100
Critical Values: {'10%': 0.347, '5%': 0.463, '2.5%': 0.574, '1%': 0.739}

<ipython-input-20-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-20-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
<ipython-input-20-d520eaee4c0b>:63: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  kpss_result = kpss(series)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'

Best ARMA model for MS:
Order: (0, 0, 0)
AIC: 405.74

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for JPM:
Order: (0, 0, 0)
AIC: 552.18

/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
/usr/local/lib/python3.11/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)
/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: An unsupported index was provided. As a result, forecasts cannot be generated. To use the model for forecasting, use one of the supported classes of index.
  self._init_dates(dates, freq)

Best ARMA model for LMT:
Order: (0, 0, 0)
AIC: 605.67

Johansen Cointegration Test:
Trace statistic: [23.67197287  7.77838754  1.02627118]
Critical values (90%, 95%, 99%): [[27.0669 29.7961 35.4628]
 [13.4294 15.4943 19.9349]
 [ 2.7055  3.8415  6.6349]]
r = 0: No cointegration at 95% confidence level
r = 1: No cointegration at 95% confidence level
r = 2: No cointegration at 95% confidence level

#@title Convert ipynb to HTML in Colab
# Upload ipynb
from google.colab import files
f = files.upload()

# Convert ipynb to html
import subprocess
file0 = list(f.keys())[0]
_ = subprocess.run(["pip", "install", "nbconvert"])
_ = subprocess.run(["jupyter", "nbconvert", file0, "--to", "html"])

# download the html
files.download(file0[:-5]+"html")

Upload widget is only available when the cell has been executed in the current browser session. Please rerun this cell to enable.

Saving Actividad_Bloomberg.ipynb to Actividad_Bloomberg.ipynb

# Install required libraries in Colab
!pip install yfinance statsmodels matplotlib pandas numpy

import numpy as np
import pandas as pd
import yfinance as yf
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller
from statsmodels.tsa.arima.model import ARIMA
import warnings
warnings.filterwarnings("ignore")

# Set random seed for reproducibility
np.random.seed(42)

# Step 1: Fetch stock data for JPM and MS from Nov 29, 2019
start_date = "2019-11-29"
end_date = "2025-02-28"

print("Fetching data for JPM...")
jpm_data = yf.download("JPM", start=start_date, end=end_date)
print("Fetching data for MS...")
ms_data = yf.download("MS", start=start_date, end=end_date)

# Extract the 'Close' column correctly from MultiIndex
jpm_prices = jpm_data[("Close", "JPM")].dropna()
ms_prices = ms_data[("Close", "MS")].dropna()
print("JPM Prices Head:\n", jpm_prices.head())
print("MS Prices Head:\n", ms_prices.head())

# Step 2: Simulate a Random Walk
def random_walk_simulation(initial_price, steps, scale=1):
    random_steps = np.random.normal(loc=0, scale=scale, size=steps)
    random_steps[0] = 0  # Start at initial price
    return initial_price + np.cumsum(random_steps)

jpm_rw = random_walk_simulation(jpm_prices.iloc[0], len(jpm_prices), scale=5)
ms_rw = random_walk_simulation(ms_prices.iloc[0], len(ms_prices), scale=5)

# Step 3: Unit Root Test (ADF)
def unit_root_test(series, name):
    result = adfuller(series.dropna())
    print(f"\nUnit Root Test (ADF) for {name}:")
    print(f"ADF Statistic: {result[0]:.4f}")
    print(f"p-value: {result[1]:.4f}")
    print("Critical Values:", {k: round(v, 4) for k, v in result[4].items()})
    if result[1] > 0.05:
        print(f"{name} likely has a unit root (non-stationary).")
    else:
        print(f"{name} does not have a unit root (stationary).")

jpm_returns = jpm_prices.pct_change().dropna()
ms_returns = ms_prices.pct_change().dropna()

unit_root_test(jpm_prices, "JPM Prices")
unit_root_test(ms_prices, "MS Prices")
unit_root_test(jpm_returns, "JPM Returns")
unit_root_test(ms_returns, "MS Returns")

# Step 4: Fit ARMA Model (ARMA(1,1))
def fit_arma(series, name):
    model = ARIMA(series, order=(1, 0, 1))
    fit = model.fit()
    print(f"\nARMA(1,1) Model Summary for {name}:")
    print(fit.summary().tables[1])
    return fit

jpm_arma = fit_arma(jpm_returns, "JPM Returns")
ms_arma = fit_arma(ms_returns, "MS Returns")

# Step 5: Plotting
plt.figure(figsize=(14, 10))

# Random Walk vs Actual Prices
plt.subplot(3, 1, 1)
plt.plot(jpm_prices.index, jpm_prices, label="JPM Actual", color="blue")
plt.plot(jpm_prices.index, jpm_rw, label="JPM Random Walk", color="orange", linestyle="--")
plt.plot(ms_prices.index, ms_prices, label="MS Actual", color="green")
plt.plot(ms_prices.index, ms_rw, label="MS Random Walk", color="red", linestyle="--")
plt.title("Stock Prices vs Random Walk Simulation")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend()

# Returns
plt.subplot(3, 1, 2)
plt.plot(jpm_returns.index, jpm_returns, label="JPM Returns", color="blue")
plt.plot(ms_returns.index, ms_returns, label="MS Returns", color="green")
plt.title("Daily Returns")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

# ARMA Forecasts (last 30 days)
jpm_forecast = jpm_arma.forecast(steps=30)
ms_forecast = ms_arma.forecast(steps=30)
forecast_index = pd.date_range(start=jpm_returns.index[-1], periods=30, freq="B")

plt.subplot(3, 1, 3)
plt.plot(jpm_returns.index[-30:], jpm_returns[-30:], label="JPM Actual Returns", color="blue")
plt.plot(forecast_index, jpm_forecast, label="JPM ARMA Forecast", color="orange", linestyle="--")
plt.plot(ms_returns.index[-30:], ms_returns[-30:], label="MS Actual Returns", color="green")
plt.plot(forecast_index, ms_forecast, label="MS ARMA Forecast", color="red", linestyle="--")
plt.title("ARMA(1,1) Forecast vs Actual Returns (Last 30 Days)")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

plt.tight_layout()
plt.show()

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Fetching data for JPM...
YF.download() has changed argument auto_adjust default to True

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Fetching data for MS...

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JPM Prices Head:
 Date
2019-11-29    113.444176
2019-12-02    113.194489
2019-12-03    111.739410
2019-12-04    113.943550
2019-12-05    114.563484
Name: (Close, JPM), dtype: float64
MS Prices Head:
 Date
2019-11-29    41.819374
2019-12-02    41.481304
2019-12-03    40.661488
2019-12-04    41.278465
2019-12-05    41.472843
Name: (Close, MS), dtype: float64

Unit Root Test (ADF) for JPM Prices:
ADF Statistic: 0.9084
p-value: 0.9932
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for MS Prices:
ADF Statistic: -0.7266
p-value: 0.8397
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for JPM Returns:
ADF Statistic: -10.5936
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Returns does not have a unit root (stationary).

Unit Root Test (ADF) for MS Returns:
ADF Statistic: -12.1755
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Returns does not have a unit root (stationary).

ARMA(1,1) Model Summary for JPM Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0008      0.001      1.592      0.111      -0.000       0.002
ar.L1         -0.6098      0.051    -12.023      0.000      -0.709      -0.510
ma.L1          0.4889      0.053      9.185      0.000       0.385       0.593
sigma2         0.0004   6.74e-06     59.204      0.000       0.000       0.000
==============================================================================

ARMA(1,1) Model Summary for MS Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0011      0.001      1.863      0.062   -5.73e-05       0.002
ar.L1         -0.6395      0.078     -8.179      0.000      -0.793      -0.486
ma.L1          0.5546      0.082      6.771      0.000       0.394       0.715
sigma2         0.0005   1.04e-05     46.906      0.000       0.000       0.001
==============================================================================

# Install required libraries in Colab
!pip install yfinance statsmodels matplotlib pandas numpy

import numpy as np
import pandas as pd
import yfinance as yf
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller, coint
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import warnings
warnings.filterwarnings("ignore")

# Set random seed for reproducibility
np.random.seed(42)

# Step 1: Fetch stock data for JPM and MS from Nov 29, 2019
start_date = "2019-11-29"
end_date = "2025-02-28"

print("Fetching data for JPM...")
jpm_data = yf.download("JPM", start=start_date, end=end_date)
print("Fetching data for MS...")
ms_data = yf.download("MS", start=start_date, end=end_date)

# Extract 'Close' prices from MultiIndex
jpm_prices = jpm_data[("Close", "JPM")].dropna()
ms_prices = ms_data[("Close", "MS")].dropna()

# Align indices for cointegration test
combined = pd.concat([jpm_prices, ms_prices], axis=1).dropna()
jpm_prices = combined.iloc[:, 0]
ms_prices = combined.iloc[:, 1]

# Step 2: Simulate a Random Walk
def random_walk_simulation(initial_price, steps, scale=1):
    random_steps = np.random.normal(loc=0, scale=scale, size=steps)
    random_steps[0] = 0
    return initial_price + np.cumsum(random_steps)

jpm_rw = random_walk_simulation(jpm_prices.iloc[0], len(jpm_prices), scale=5)
ms_rw = random_walk_simulation(ms_prices.iloc[0], len(ms_prices), scale=5)

# Step 3: Unit Root Test (ADF)
def unit_root_test(series, name):
    result = adfuller(series.dropna())
    print(f"\nUnit Root Test (ADF) for {name}:")
    print(f"ADF Statistic: {result[0]:.4f}")
    print(f"p-value: {result[1]:.4f}")
    print("Critical Values:", {k: round(v, 4) for k, v in result[4].items()})
    if result[1] > 0.05:
        print(f"{name} likely has a unit root (non-stationary).")
    else:
        print(f"{name} does not have a unit root (stationary).")

jpm_returns = jpm_prices.pct_change().dropna()
ms_returns = ms_prices.pct_change().dropna()

unit_root_test(jpm_prices, "JPM Prices")
unit_root_test(ms_prices, "MS Prices")
unit_root_test(jpm_returns, "JPM Returns")
unit_root_test(ms_returns, "MS Returns")

# Step 4: Fit ARMA Model (ARMA(1,1))
def fit_arma(series, name):
    model = ARIMA(series, order=(1, 0, 1))
    fit = model.fit()
    print(f"\nARMA(1,1) Model Summary for {name}:")
    print(fit.summary().tables[1])
    return fit

jpm_arma = fit_arma(jpm_returns, "JPM Returns")
ms_arma = fit_arma(ms_returns, "MS Returns")

# Step 5: Correlogram and Partial Correlogram of Residuals
plt.figure(figsize=(12, 8))

plt.subplot(2, 2, 1)
plot_acf(jpm_arma.resid, ax=plt.gca(), title="ACF of JPM ARMA Residuals")
plt.subplot(2, 2, 2)
plot_pacf(jpm_arma.resid, ax=plt.gca(), title="PACF of JPM ARMA Residuals")
plt.subplot(2, 2, 3)
plot_acf(ms_arma.resid, ax=plt.gca(), title="ACF of MS ARMA Residuals")
plt.subplot(2, 2, 4)
plot_pacf(ms_arma.resid, ax=plt.gca(), title="PACF of MS ARMA Residuals")
plt.tight_layout()
plt.show()

# Step 6: Cointegration Test (Engle-Granger)
print("\nCointegration Test (Engle-Granger) between JPM and MS Prices:")
coint_result = coint(jpm_prices, ms_prices)
print(f"Cointegration Test Statistic: {coint_result[0]:.4f}")
print(f"p-value: {coint_result[1]:.4f}")
print("Critical Values:", {k: round(v, 4) for k, v in zip(['1%', '5%', '10%'], coint_result[2])})
if coint_result[1] < 0.05:
    print("Result: Reject the null hypothesis - JPM and MS prices are cointegrated.")
else:
    print("Result: Fail to reject the null hypothesis - JPM and MS prices are not cointegrated.")

# Step 7: Plotting Original Analyses
plt.figure(figsize=(14, 10))

# Random Walk vs Actual Prices
plt.subplot(3, 1, 1)
plt.plot(jpm_prices.index, jpm_prices, label="JPM Actual", color="blue")
plt.plot(jpm_prices.index, jpm_rw, label="JPM Random Walk", color="orange", linestyle="--")
plt.plot(ms_prices.index, ms_prices, label="MS Actual", color="green")
plt.plot(ms_prices.index, ms_rw, label="MS Random Walk", color="red", linestyle="--")
plt.title("Stock Prices vs Random Walk Simulation")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend()

# Returns
plt.subplot(3, 1, 2)
plt.plot(jpm_returns.index, jpm_returns, label="JPM Returns", color="blue")
plt.plot(ms_returns.index, ms_returns, label="MS Returns", color="green")
plt.title("Daily Returns")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

# ARMA Forecasts (last 30 days)
jpm_forecast = jpm_arma.forecast(steps=30)
ms_forecast = ms_arma.forecast(steps=30)
forecast_index = pd.date_range(start=jpm_returns.index[-1], periods=30, freq="B")

plt.subplot(3, 1, 3)
plt.plot(jpm_returns.index[-30:], jpm_returns[-30:], label="JPM Actual Returns", color="blue")
plt.plot(forecast_index, jpm_forecast, label="JPM ARMA Forecast", color="orange", linestyle="--")
plt.plot(ms_returns.index[-30:], ms_returns[-30:], label="MS Actual Returns", color="green")
plt.plot(forecast_index, ms_forecast, label="MS ARMA Forecast", color="red", linestyle="--")
plt.title("ARMA(1,1) Forecast vs Actual Returns (Last 30 Days)")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

plt.tight_layout()
plt.show()

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Fetching data for JPM...
Fetching data for MS...

Unit Root Test (ADF) for JPM Prices:
ADF Statistic: 0.9084
p-value: 0.9932
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for MS Prices:
ADF Statistic: -0.7266
p-value: 0.8397
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for JPM Returns:
ADF Statistic: -10.5936
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Returns does not have a unit root (stationary).

Unit Root Test (ADF) for MS Returns:
ADF Statistic: -12.1755
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Returns does not have a unit root (stationary).

ARMA(1,1) Model Summary for JPM Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0008      0.001      1.592      0.111      -0.000       0.002
ar.L1         -0.6098      0.051    -12.023      0.000      -0.709      -0.510
ma.L1          0.4889      0.053      9.185      0.000       0.385       0.593
sigma2         0.0004   6.74e-06     59.204      0.000       0.000       0.000
==============================================================================

ARMA(1,1) Model Summary for MS Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0011      0.001      1.863      0.062   -5.73e-05       0.002
ar.L1         -0.6395      0.078     -8.179      0.000      -0.793      -0.486
ma.L1          0.5546      0.082      6.771      0.000       0.394       0.715
sigma2         0.0005   1.04e-05     46.906      0.000       0.000       0.001
==============================================================================

Cointegration Test (Engle-Granger) between JPM and MS Prices:
Cointegration Test Statistic: -1.5886
p-value: 0.7257
Critical Values: {'1%': -3.9048, '5%': -3.3408, '10%': -3.0477}
Result: Fail to reject the null hypothesis - JPM and MS prices are not cointegrated.

# Install required libraries in Colab
!pip install yfinance statsmodels matplotlib pandas numpy

import numpy as np
import pandas as pd
import yfinance as yf
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller, coint
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import warnings
warnings.filterwarnings("ignore")

# Set random seed for reproducibility
np.random.seed(42)

# Step 1: Fetch stock data for JPM and MS from Nov 29, 2019
start_date = "2019-11-29"
end_date = "2025-02-28"

print("Fetching data for JPM...")
jpm_data = yf.download("JPM", start=start_date, end=end_date)
print("Fetching data for MS...")
ms_data = yf.download("MS", start=start_date, end=end_date)

# Extract 'Close' prices from MultiIndex
jpm_prices = jpm_data['Close'].dropna()
ms_prices = ms_data['Close'].dropna()

# Align indices for cointegration test
combined = pd.concat([jpm_prices, ms_prices], axis=1).dropna()
jpm_prices = combined.iloc[:, 0]
ms_prices = combined.iloc[:, 1]

# Step 2: Simulate a Random Walk
def random_walk_simulation(initial_price, steps, scale=1):
    random_steps = np.random.normal(loc=0, scale=scale, size=steps)
    random_steps[0] = 0
    return initial_price + np.cumsum(random_steps)

jpm_rw = random_walk_simulation(jpm_prices.iloc[0], len(jpm_prices), scale=5)
ms_rw = random_walk_simulation(ms_prices.iloc[0], len(ms_prices), scale=5)

# Step 3: Unit Root Test (ADF)
def unit_root_test(series, name):
    result = adfuller(series.dropna())
    print(f"\nUnit Root Test (ADF) for {name}:")
    print(f"ADF Statistic: {result[0]:.4f}")
    print(f"p-value: {result[1]:.4f}")
    print("Critical Values:", {k: round(v, 4) for k, v in result[4].items()})
    if result[1] > 0.05:
        print(f"{name} likely has a unit root (non-stationary).")
    else:
        print(f"{name} does not have a unit root (stationary).")

jpm_returns = jpm_prices.pct_change().dropna()
ms_returns = ms_prices.pct_change().dropna()

unit_root_test(jpm_prices, "JPM Prices")
unit_root_test(ms_prices, "MS Prices")
unit_root_test(jpm_returns, "JPM Returns")
unit_root_test(ms_returns, "MS Returns")

# Step 4: Fit ARMA Model (ARMA(1,1))
def fit_arma(series, name):
    model = ARIMA(series, order=(1, 0, 1))
    fit = model.fit()
    print(f"\nARMA(1,1) Model Summary for {name}:")
    print(fit.summary().tables[1])
    return fit

jpm_arma = fit_arma(jpm_returns, "JPM Returns")
ms_arma = fit_arma(ms_returns, "MS Returns")

# Step 5: Correlogram and Partial Correlogram of Residuals
plt.figure(figsize=(12, 8))

plt.subplot(2, 2, 1)
plot_acf(jpm_arma.resid, ax=plt.gca(), title="ACF of JPM ARMA Residuals")
plt.subplot(2, 2, 2)
plot_pacf(jpm_arma.resid, ax=plt.gca(), title="PACF of JPM ARMA Residuals")
plt.subplot(2, 2, 3)
plot_acf(ms_arma.resid, ax=plt.gca(), title="ACF of MS ARMA Residuals")
plt.subplot(2, 2, 4)
plot_pacf(ms_arma.resid, ax=plt.gca(), title="PACF of MS ARMA Residuals")
plt.tight_layout()
plt.show()

# Step 6: Cointegration Test (Engle-Granger)
print("\nCointegration Test (Engle-Granger) between JPM and MS Prices:")
coint_result = coint(jpm_prices, ms_prices)
print(f"Cointegration Test Statistic: {coint_result[0]:.4f}")
print(f"p-value: {coint_result[1]:.4f}")
print("Critical Values:", {k: round(v, 4) for k, v in zip(['1%', '5%', '10%'], coint_result[2])})
if coint_result[1] < 0.05:
    print("Result: Reject the null hypothesis - JPM and MS prices are cointegrated.")
else:
    print("Result: Fail to reject the null hypothesis - JPM and MS prices are not cointegrated.")

# Step 7: Plotting Original Analyses
plt.figure(figsize=(14, 10))

# Random Walk vs Actual Prices
plt.subplot(3, 1, 1)
plt.plot(jpm_prices.index, jpm_prices, label="JPM Actual", color="blue")
plt.plot(jpm_prices.index, jpm_rw, label="JPM Random Walk", color="orange", linestyle="--")
plt.plot(ms_prices.index, ms_prices, label="MS Actual", color="green")
plt.plot(ms_prices.index, ms_rw, label="MS Random Walk", color="red", linestyle="--")
plt.title("Stock Prices vs Random Walk Simulation")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend()

# Returns
plt.subplot(3, 1, 2)
plt.plot(jpm_returns.index, jpm_returns, label="JPM Returns", color="blue")
plt.plot(ms_returns.index, ms_returns, label="MS Returns", color="green")
plt.title("Daily Returns")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

# ARMA Forecasts (last 30 days)
jpm_forecast = jpm_arma.forecast(steps=30)
ms_forecast = ms_arma.forecast(steps=30)
forecast_index = pd.date_range(start=jpm_returns.index[-1], periods=30, freq="B")

plt.subplot(3, 1, 3)
plt.plot(jpm_returns.index[-30:], jpm_returns[-30:], label="JPM Actual Returns", color="blue")
plt.plot(forecast_index, jpm_forecast, label="JPM ARMA Forecast", color="orange", linestyle="--")
plt.plot(ms_returns.index[-30:], ms_returns[-30:], label="MS Actual Returns", color="green")
plt.plot(forecast_index, ms_forecast, label="MS ARMA Forecast", color="red", linestyle="--")
plt.title("ARMA(1,1) Forecast vs Actual Returns (Last 30 Days)")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

plt.tight_layout()
plt.show()

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Fetching data for JPM...
Fetching data for MS...

Unit Root Test (ADF) for JPM Prices:
ADF Statistic: 0.9084
p-value: 0.9932
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for MS Prices:
ADF Statistic: -0.7266
p-value: 0.8397
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for JPM Returns:
ADF Statistic: -10.5936
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Returns does not have a unit root (stationary).

Unit Root Test (ADF) for MS Returns:
ADF Statistic: -12.1755
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Returns does not have a unit root (stationary).

ARMA(1,1) Model Summary for JPM Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0008      0.001      1.592      0.111      -0.000       0.002
ar.L1         -0.6098      0.051    -12.023      0.000      -0.709      -0.510
ma.L1          0.4889      0.053      9.185      0.000       0.385       0.593
sigma2         0.0004   6.74e-06     59.204      0.000       0.000       0.000
==============================================================================

ARMA(1,1) Model Summary for MS Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0011      0.001      1.863      0.062   -5.73e-05       0.002
ar.L1         -0.6395      0.078     -8.179      0.000      -0.793      -0.486
ma.L1          0.5546      0.082      6.771      0.000       0.394       0.715
sigma2         0.0005   1.04e-05     46.906      0.000       0.000       0.001
==============================================================================

Cointegration Test (Engle-Granger) between JPM and MS Prices:
Cointegration Test Statistic: -1.5886
p-value: 0.7257
Critical Values: {'1%': -3.9048, '5%': -3.3408, '10%': -3.0477}
Result: Fail to reject the null hypothesis - JPM and MS prices are not cointegrated.

# Install required libraries in Colab
!pip install yfinance statsmodels matplotlib pandas numpy

import numpy as np
import pandas as pd
import yfinance as yf
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller, coint
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import warnings
warnings.filterwarnings("ignore")

# Set random seed for reproducibility
np.random.seed(42)

# Step 1: Fetch stock data for JPM and MS from Nov 29, 2019
start_date = "2019-11-29"
end_date = "2025-02-28"

print("Fetching data for JPM...")
jpm_data = yf.download("JPM", start=start_date, end=end_date)
print("Fetching data for MS...")
ms_data = yf.download("MS", start=start_date, end=end_date)

# Extract 'Close' prices from MultiIndex
jpm_prices = jpm_data['Close'].dropna()
ms_prices = ms_data['Close'].dropna()

# Align indices for cointegration test
combined = pd.concat([jpm_prices, ms_prices], axis=1).dropna()
jpm_prices = combined.iloc[:, 0]
ms_prices = combined.iloc[:, 1]

# Step 2: Simulate a Random Walk
def random_walk_simulation(initial_price, steps, scale=1):
    random_steps = np.random.normal(loc=0, scale=scale, size=steps)
    random_steps[0] = 0
    return initial_price + np.cumsum(random_steps)

jpm_rw = random_walk_simulation(jpm_prices.iloc[0], len(jpm_prices), scale=5)
ms_rw = random_walk_simulation(ms_prices.iloc[0], len(ms_prices), scale=5)

# Step 3: Unit Root Test (ADF)
def unit_root_test(series, name):
    result = adfuller(series.dropna())
    print(f"\nUnit Root Test (ADF) for {name}:")
    print(f"ADF Statistic: {result[0]:.4f}")
    print(f"p-value: {result[1]:.4f}")
    print("Critical Values:", {k: round(v, 4) for k, v in result[4].items()})
    if result[1] > 0.05:
        print(f"{name} likely has a unit root (non-stationary).")
    else:
        print(f"{name} does not have a unit root (stationary).")

jpm_returns = jpm_prices.pct_change().dropna()
ms_returns = ms_prices.pct_change().dropna()

unit_root_test(jpm_prices, "JPM Prices")
unit_root_test(ms_prices, "MS Prices")
unit_root_test(jpm_returns, "JPM Returns")
unit_root_test(ms_returns, "MS Returns")

# Step 4: Fit ARMA Model (ARMA(1,1))
def fit_arma(series, name):
    model = ARIMA(series, order=(1, 0, 1))
    fit = model.fit()
    print(f"\nARMA(1,1) Model Summary for {name}:")
    print(fit.summary().tables[1])
    return fit

jpm_arma = fit_arma(jpm_returns, "JPM Returns")
ms_arma = fit_arma(ms_returns, "MS Returns")

# Step 5: Correlogram and Partial Correlogram of Residuals
plt.figure(figsize=(12, 8))

plt.subplot(2, 2, 1)
plot_acf(jpm_arma.resid, ax=plt.gca(), title="ACF of JPM ARMA Residuals")
plt.subplot(2, 2, 2)
plot_pacf(jpm_arma.resid, ax=plt.gca(), title="PACF of JPM ARMA Residuals")
plt.subplot(2, 2, 3)
plot_acf(ms_arma.resid, ax=plt.gca(), title="ACF of MS ARMA Residuals")
plt.subplot(2, 2, 4)
plot_pacf(ms_arma.resid, ax=plt.gca(), title="PACF of MS ARMA Residuals")
plt.tight_layout()
plt.show()

# Step 6: Cointegration Test (Engle-Granger)
print("\nCointegration Test (Engle-Granger) between JPM and MS Prices:")
coint_result = coint(jpm_prices, ms_prices)
print(f"Cointegration Test Statistic: {coint_result[0]:.4f}")
print(f"p-value: {coint_result[1]:.4f}")
print("Critical Values:", {k: round(v, 4) for k, v in zip(['1%', '5%', '10%'], coint_result[2])})
if coint_result[1] < 0.05:
    print("Result: Reject the null hypothesis - JPM and MS prices are cointegrated.")
else:
    print("Result: Fail to reject the null hypothesis - JPM and MS prices are not cointegrated.")

# Step 7: Plotting Original Analyses
plt.figure(figsize=(14, 10))

# Random Walk vs Actual Prices
plt.subplot(3, 1, 1)
plt.plot(jpm_prices.index, jpm_prices, label="JPM Actual", color="blue")
plt.plot(jpm_prices.index, jpm_rw, label="JPM Random Walk", color="orange", linestyle="--")
plt.plot(ms_prices.index, ms_prices, label="MS Actual", color="green")
plt.plot(ms_prices.index, ms_rw, label="MS Random Walk", color="red", linestyle="--")
plt.title("Stock Prices vs Random Walk Simulation")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend()

# Returns
plt.subplot(3, 1, 2)
plt.plot(jpm_returns.index, jpm_returns, label="JPM Returns", color="blue")
plt.plot(ms_returns.index, ms_returns, label="MS Returns", color="green")
plt.title("Daily Returns")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

# ARMA Forecasts (last 30 days)
jpm_forecast = jpm_arma.forecast(steps=30)
ms_forecast = ms_arma.forecast(steps=30)
forecast_index = pd.date_range(start=jpm_returns.index[-1], periods=30, freq="B")

plt.subplot(3, 1, 3)
plt.plot(jpm_returns.index[-30:], jpm_returns[-30:], label="JPM Actual Returns", color="blue")
plt.plot(forecast_index, jpm_forecast, label="JPM ARMA Forecast", color="orange", linestyle="--")
plt.plot(ms_returns.index[-30:], ms_returns[-30:], label="MS Actual Returns", color="green")
plt.plot(forecast_index, ms_forecast, label="MS ARMA Forecast", color="red", linestyle="--")
plt.title("ARMA(1,1) Forecast vs Actual Returns (Last 30 Days)")
plt.xlabel("Date")
plt.ylabel("Returns")
plt.legend()

plt.tight_layout()
plt.show()

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Fetching data for JPM...
Fetching data for MS...

Unit Root Test (ADF) for JPM Prices:
ADF Statistic: 0.9084
p-value: 0.9932
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for MS Prices:
ADF Statistic: -0.7266
p-value: 0.8397
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Prices likely has a unit root (non-stationary).

Unit Root Test (ADF) for JPM Returns:
ADF Statistic: -10.5936
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.568}
JPM Returns does not have a unit root (stationary).

Unit Root Test (ADF) for MS Returns:
ADF Statistic: -12.1755
p-value: 0.0000
Critical Values: {'1%': -3.4354, '5%': -2.8638, '10%': -2.5679}
MS Returns does not have a unit root (stationary).

ARMA(1,1) Model Summary for JPM Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0008      0.001      1.592      0.111      -0.000       0.002
ar.L1         -0.6098      0.051    -12.023      0.000      -0.709      -0.510
ma.L1          0.4889      0.053      9.185      0.000       0.385       0.593
sigma2         0.0004   6.74e-06     59.204      0.000       0.000       0.000
==============================================================================

ARMA(1,1) Model Summary for MS Returns:
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0011      0.001      1.863      0.062   -5.73e-05       0.002
ar.L1         -0.6395      0.078     -8.179      0.000      -0.793      -0.486
ma.L1          0.5546      0.082      6.771      0.000       0.394       0.715
sigma2         0.0005   1.04e-05     46.906      0.000       0.000       0.001
==============================================================================

Cointegration Test (Engle-Granger) between JPM and MS Prices:
Cointegration Test Statistic: -1.5886
p-value: 0.7257
Critical Values: {'1%': -3.9048, '5%': -3.3408, '10%': -3.0477}
Result: Fail to reject the null hypothesis - JPM and MS prices are not cointegrated.

import yfinance as yf
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller

# Define the stock symbol and date range
stock_symbol = 'JPM'
start_date = '2019-11-29'
end_date = '2025-02-25'

# Fetch historical stock data
stock_data = yf.download(stock_symbol, start=start_date, end=end_date)
stock_data['Close'].plot(title=f'{stock_symbol} Stock Price', figsize=(10, 6))
plt.show()

# Perform the Augmented Dickey-Fuller test
result = adfuller(stock_data['Close'])
print('ADF Statistic:', result[0])
print('p-value:', result[1])
for key, value in result[4].items():
    print('Critial Values:')
    print(f'   {key}, {value}')

# Calculate moving averages
stock_data['MA9'] = stock_data['Close'].rolling(window=9).mean()
stock_data['MA30'] = stock_data['Close'].rolling(window=30).mean()

# Plot the stock prices along with moving averages
plt.figure(figsize=(14, 7))
plt.plot(stock_data['Close'], label='Close Price')
plt.plot(stock_data['MA9'], label='9-Day Moving Average')
plt.plot(stock_data['MA30'], label='30-Day Moving Average')
plt.title(f'{stock_symbol} Moving Averages')
plt.xlabel('Date')
plt.ylabel('Price')
plt.legend()
plt.show()

[*********************100%***********************]  1 of 1 completed

ADF Statistic: 0.9078740238940189
p-value: 0.9931922288781313
Critial Values:
   1%, -3.435374708138995
Critial Values:
   5%, -2.863758995766637
Critial Values:
   10%, -2.5679514065499265

import yfinance as yf
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller

# Define the stock symbol and date range
stock_symbol = 'LMT'
start_date = '2019-11-29'
end_date = '2025-02-25'

# Fetch historical stock data
stock_data = yf.download(stock_symbol, start=start_date, end=end_date)
stock_data['Close'].plot(title=f'{stock_symbol} Stock Price', figsize=(10, 6))
plt.show()

# Perform the Augmented Dickey-Fuller test
result = adfuller(stock_data['Close'])
print('ADF Statistic:', result[0])
print('p-value:', result[1])
for key, value in result[4].items():
    print('Critial Values:')
    print(f'   {key}, {value}')

# Calculate moving averages
stock_data['MA9'] = stock_data['Close'].rolling(window=9).mean()
stock_data['MA30'] = stock_data['Close'].rolling(window=30).mean()

# Plot the stock prices along with moving averages
plt.figure(figsize=(14, 7))
plt.plot(stock_data['Close'], label='Close Price')
plt.plot(stock_data['MA9'], label='9-Day Moving Average')
plt.plot(stock_data['MA30'], label='30-Day Moving Average')
plt.title(f'{stock_symbol} Moving Averages')
plt.xlabel('Date')
plt.ylabel('Price')
plt.legend()
plt.show()

[*********************100%***********************]  1 of 1 completed

ADF Statistic: -1.6351905924221362
p-value: 0.4647749369877407
Critial Values:
   1%, -3.435336393256612
Critial Values:
   5%, -2.863742089354917
Critial Values:
   10%, -2.5679424031562683

import yfinance as yf
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller

# Define the stock symbol and date range
stock_symbol = 'MS'
start_date = '2019-11-29'
end_date = '2025-02-25'

# Fetch historical stock data
stock_data = yf.download(stock_symbol, start=start_date, end=end_date)
stock_data['Close'].plot(title=f'{stock_symbol} Stock Price', figsize=(10, 6))
plt.show()

# Perform the Augmented Dickey-Fuller test
result = adfuller(stock_data['Close'])
print('ADF Statistic:', result[0])
print('p-value:', result[1])
for key, value in result[4].items():
    print('Critial Values:')
    print(f'   {key}, {value}')

# Calculate moving averages
stock_data['MA9'] = stock_data['Close'].rolling(window=9).mean()
stock_data['MA30'] = stock_data['Close'].rolling(window=30).mean()

# Plot the stock prices along with moving averages
plt.figure(figsize=(14, 7))
plt.plot(stock_data['Close'], label='Close Price')
plt.plot(stock_data['MA9'], label='9-Day Moving Average')
plt.plot(stock_data['MA30'], label='30-Day Moving Average')
plt.title(f'{stock_symbol} Moving Averages')
plt.xlabel('Date')
plt.ylabel('Price')
plt.legend()
plt.show()

[*********************100%***********************]  1 of 1 completed

ADF Statistic: -0.6641436071548955
p-value: 0.8558198685249957
Critial Values:
   1%, -3.435340198430096
Critial Values:
   5%, -2.863743768394356
Critial Values:
   10%, -2.567943297315671